Reduction Factors for O(N)⊃O(NK-1)

In terms of the concept of irreducible tensor basis and the properties of irreducible tensor operator, we give, by mathematical induction, the irreducible representations of O(N) for (m_1Nm_2N...m_[N/2]N) and all reduction factors of O(N)⊃O(N-1) for (1 0...0)⊗(m_1Nm_2N...m_[N/2]N)     

Spinor Representation Reduction Factors for O(N) ⊃ O(N - 1)

In this paper, the spinor irreducible representations of O (N) for (σ 1/2 1/2 ± 1/2) with some O (N) U-functions, are obtained by the building-up process.     

The Branching Rules for U(7)⊃0(7)⊃G2⊃0(3)

The branching rules for U(7)⊃0(7)⊃G₂ and G₂⊃0(3) for at most fourcolumned IRs of U(7)) and O(7) are given respectively by using the method of decomposition of Kronecker products of IRs of groups. The needed formulae for decomposition of Kronecker products of IRs of O(7) and G₂ are given also.     

On the Boson Representations of SU(3) Algebra in the Basis SU(3)⊃U(1)+U(1)

The Dyson and Holstein-Primakoff boson realizations of the generators of SU(3) algebra have been given for the algebra chain SU(3)⊃U(1)+U(1), and a set of recursion formulae of the transformation matrix, which turn the Dyson onto the Holstein-. Primakoff representation, have been presented. The multiplicity that can occur in the reduction of SU(3)⊃U(1)+U(1) is naturally determined.     

DYNKIN'S EMBEDDING METHOD AND SUBALGEBRA CHAINS OF U(6)⊃SU(3)*

Use Dynkin's embedding method to find out the generators of two subalgebra chains of U(6)⊃SU(3).     

Yang-Baxterization and New Solutions Associated with SU(2) Tensorial Space Vj⊗V1/2*

By applying extended diagrammatic technique to SU(2) tensorial space V^j⊗V^1/2 new solutions of the correspondent braid group representations and their Yang-Baxterization are established. The explicit forms of the new solutions of Yang-Baxter equation for j = 1 are given. Through this example the general feature of this new type of solutions is figured out.     

Inhomogeneous q-Differential Realization,Inhomogeneous q-Boson Realization of Quantum Group SU(n)q and Its Indecomposable Representations

An inhomogeneous q-differential realization (q-IHDR) and its corresponding inhomogeneous q-boson realization (q-IHBR) of quantum group SU(n)_q are studied. By making use of the q-IHBR a kind of infinite dimensional indecomposable and irreducible representations of SU(n)_q is studied on the q-Fcck space. The finite dimensional irreducible representations of SU(n), are obtained on the finite dimensional subspaces of q-Fock space. As an example, these representations of SU(2)_q are studied in detail and Jimbo standard irreducible representations are obtained.     

A new solution of d = 11 supergravity with internal isometry group SU(3) × SU(2) × U(1)

A new solution of the bosonic sector of D = 11 supergravity is presented in which the internal space has the topology CP² × S² × S¹ and the internal isometry group is SU(3) × SU(2) × U(1).     

The hidden SO(4) symmetry of general SU(2) thirring models

General four-fermion interactions in two dimensions with SU(2) invariance are shown to possess a hidden SO(4) symmetry. As a consequence physical states belong to irreducible representations of the two commuting O(3) subgroups and their interactions decouple accordingly. Two independnet stable trajectories of the renormalization group are shown to exist perturbatively and are consistently reproduced by abelian bosonization.     

FOUR-FERMION SU(N)HYPERCOLOR CONDENSATES AND THEIR MASS SCALES

It is conjectured and shown by means of the screening Casimir effective couplings among fer-mions that,the four-fermivn condensates<(ff)²> formed through the SU(N).hypercolor gauge interac-tions,in geneial,may always have two forming paths which respectively correspond to different mass scales, and only for some special SU(N) representations of the fermions f the condensates have one mass scale or no four-fermion condensate could be formed.     

The Fractional Parentage Coefficients for a Double-j Fermion System

The coefficients of fractional parentage (CFPs) for a double-j fermion system are defined. The CFPs are given when the wave functions are classified according to the group chains U(N) ⊃ U(N₁) × U(N₂) ⊃ SP(N₁)× SP(N₂) ⊃O(3₁)×O(3₂) ⊃ O(3) and U(N) ⊃ SP(N) ⊃ SP(N₁)× SP(N₂) ⊃ O(3₁)× O(3₂) ⊃ O(3). Using these CFPs many repeating calculations can be avoided.     

Coherent states associated with the groups SU(N) and SU(N, 1)

The coherent-state basis is constructed for symmetric representations of the groups SU(N) and SU(N, 1) and its properties are studied. The evolution of coherent states is considered. A relationship between the SU(N) coherent states and the Glauber coherent states is established.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 83–89, January, 1990.     

Irreducible Representations and Reduced Coefficients of Quantum Algebra SUq(4) in the SUq(4)⊃ SUq(2)⊕SUq(2) Basis

In this paper, the tensor-like method is presented, and the applications to quantum algebra SU_q(4) are given. The irreducible representation of SU_q(4) and a recurrent formula to calculate reduced coefficients of SU_q(4)⊃ SU_q(2)⊕SU_q(2) is obtained. Some of reduced matrix elements and q-reduced scalar factors (qRF) are tabulated.     

Two-Parameter Deformations of SU(2) and SU (1,l) Algebras

The algebras SU(2) and SU(1,1) are promoted to two-parameter quantum universal enveloping algebras (QUEA) by a doubleparameter deformation in this paper. The discrete unitary irreducible representations and their deformed coherent states are studied. The deformed generators are given by a Jordan-Schwinger realization and a Bargmann-Fock representation. It is also interesting that the two-parameter deformed coherent states are found to relate to the oneparameter deformed ones by a simple scaling transformation and this can be used to derive the completeness relation of the former.     

Astrophysical Rates for ¹²N(p,)¹³O Direct Capture Reaction

The proton capture on the unstable nuclei plays a very important role in nucleonsynthesis. The ¹²N(p,)¹³O reaction rates at the energies of astrophysical interest are estimated with the spectroscopic factor and asymptotic normalization coefficient methods. The present results show that the ¹²N(p,)¹³O reaction may play an important role in x-ray bursts.     

Excited glueball states in four-dimensional SU(3) lattice gauge theory

For SU(N) (N ? 2) lattice gauge theories in four dimensions we construct all irreducible representations of the full cubic group on spacelike Wilson loop operators up to length 6. Relying on this set of operators preliminary Monte Carlo results for SU(3) excited glueball states are reported.     

Irreducible representations of the quantum analogue of SU(2)

We give the complete set of irreducible representations of U(SU(2))_q when q is a mth root of unity. In particular, we show that their dimensions are less or equal to m. Some of them are not highest-weight representations.     

Linearized N = 2 supergravity in terms of SU(2)-extended superfields

The linearized theory of N = 2 conformai supergravity is expressed in terms of a single irreducible SU(2)-extended superfield. In particular, in this way the origin of the N = 2 superconformal multiplet is established.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, No. 5, pp. 93–95, May, 1986.     

The orthonormal basis for symmetric irreducible representations of O(5) × SU(1, 1) and its application to the interacting boson model

A main result of the paper is a constructed orthonormal basis for symmetric irreducible representations of the direct group product O(5) × SU(1, 1). Orthonormality is an aim achieved for the first time for this case. The construction was formed from the point of view of its application to the interacting boson approximation in nuclear theory. In this case calculations of matrix elements of physical operators are much simplified because the constructed basis is expressed as linear combinations of the simplest states of the boson harmonic oscillator basis. A couple of examples of such calculations are also demonstrated in the paper.     

Chiral Ring Structure in the N = 2 Superconformal Field Theory Based on the Coset Construction with SU(1,1)/U(1)

In this paper, we carefully analyze the unitarity of the simplest Kazama-Suzuki model based on the noncompact group. The chiral ring structure in this N = 2 theory is clarified. In general, it is infinitely dimensional and innumerable. The primary chiral states belonging to the ring can be constructed by means of the direct products of the highest weight states of the coset SU(1,1)/ U(1) and the scalar representation of U(1) for the fermions. The primary chird and anti-chiral states Jive individually in the positive discrete series D⁺ and negative discrete series D^- of SU(1,1), respectively. With appropriate restrictions, this theory can be regarded as one at the fixed point of a Landau-Ginzburg theory, in which the superpotential is given by S₁₂ in the fourteen exceptional singularities.